Q1. The pair of equations $x = a$ and $y = b$ graphically represents lines which are:
Q2. A father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages (in years) of the son and the father are:
Q3. The value of $k$ for which the system of equations $x + 2y = 3$ and $5x + ky + 7 = 0$ has a unique solution is:
Q4. If $2x + 3y = 11$ and $2x - 4y = -24$, then the value of $m$ for which $y = mx + 3$ is:
Q5. Assertion (A): The linear equations $x - 2y - 3 = 0$ and $3x - 6y - 9 = 0$ represent coincident lines. Reason (R): For coincident lines $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.
Q6. 5 books and 7 pens cost ₹ 79. 7 books and 5 pens cost ₹ 77. Find the cost of 1 book and 2 pens.
Solve on white paper.
Q7. In a $\Delta ABC$, $\angle C = 3 \angle B = 2(\angle A + \angle B)$. Find the three angles.
Q8. Solve for $x$ and $y$: $99x + 101y = 499$, $101x + 99y = 501$.
Q9. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Q10. The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them manages to save ₹ 2000 per month, find their monthly incomes.
Q11. Case Study: Book Fair
At a book fair, the entry ticket for adults is ₹ $x$ and for children is ₹ $y$. A family of 2 adults and 3 children paid ₹ 350 for entry. Another family of 1 adult and 2 children paid ₹ 200.
(i) Represent this situation algebraically.
(ii) Find the entry fee for an Adult and a Child.
(iii) Calculate the cost for a group of 4 Adults and 5 Children.
Q12. Case Study: Highway Travel
Two places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour.
(i) Form the pair of linear equations representing the situation.
(ii) Find the speeds of the two cars.
(iii) What is the distance covered by the car starting from A when they meet in the same direction?